The difference in time scale is crucial though. For the past 2000 years, sea level hadn't changed much at all[1]. If the city has to move to adapt to changing coastlines, it can probably manage the move over millennia.

With climate change, we're looking at drastic coastline changes over the next 100 years. 100 years is extremely short for cities - it probably takes about that to go from being a town to being a city, if you have excellent growth rates.

To move a city in 100 years is probably flat-out impossible, just for cost reasons alone. Most cities are hard-pressed to pay for maintenance of roads and essential services, and service their already crushing debt levels. City governments are not going to manage it, which means the citizens of the cities are going to shoulder the costs. We're going to see large-scale financial hardship in coastal cities going forward, and multiple cities going bankrupt and into decline.

[1] https://ocean.si.edu/through-time/ancient-seas/sea-level-ris...